Pluton,
Here is your plot. I used ParametricPlot3D to draw the surface.
Needs["Graphics`Colors`"]
f[s_, t_] := 4s t
ParametricPlot3D[{s, w - s w, -4 (-1 + s) s w}, {s, 0, 1}, {w, 0, 1},
PlotPoints -> 15,
BoxRatios -> {1, 1, 1/2},
AxesLabel -> {s, t, f},
PlotLabel -> SequenceForm[f[s, t], " on a Triangular Domain"],
ViewPoint -> {2.292, -1.483, 2.000},
Background -> Linen,
ImageSize -> 450];
Notice that I used a reparametrization of the function, and of t so that the
plot statement now uses fixed iterators. (Plot does not allow dependent
iterators such as are allowed in Integrate.) How did I get the
reparametrization? By using the IteratorSubstitution routine from the
DrawGraphics package. It replaces t by a new variable w that has a fixed
iteration range.
Needs["DrawGraphics`DrawingMaster`"]
IteratorSubstitution[{s, t, f[s, t]}, {t, 0, 1 - s}]
{{s, w - s w, -4 (-1 + s) s w}, {w, 0, 1}}
The first item above is the new parametrization of the surface in terms of s
and w, and the second item is the w iterator.
David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/
From: pluton [mailto:plutonesque at gmail.com]
To: mathgroup at smc.vnet.net
Hi there,
I want to plot the following function f = 4*s*t over a triangle defined
by s going from 0 to 1
and t from 0 to 1-s.
I tried Plot3D[4st, {s, 0, 1}, {t, 0, 1-s}]; but it does not work. Any
suggestion ?
Thank you,
Pluton